Should synthetic forward price be used to calculate implied volatility for cash product only??

[tesla1060]

Hi,



Assuming option market moves faster than etf cash price in intraday high frequency setting. That means at each time point, when implied volatility is calculated by black-schole model by using cash etf price, that is a small portion of dIV (change of IV) is due to that etf price hasnt caught up with option price.



So in this sense, I feel that if I want to build a volatility curve on etf, I should in fact use synthetic forward price from put-call parity and employ black formula?



Not very sure if my understanding is correct.

[athletico]

Are the etf options european? If so, then you can use the implied forward the way you describe. Otherwise, it's not that simple because option prices have early ex premium baked in.